Scott Vernon climbed off the bench to fire the hat-trick that sunk Falkirk's League Cup ambitions but Aberdeen boss Derek McInnes admitted the striker was only handed an early run out because Calvin Zola was flirting with a red card.
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The former Burton Albion frontman was chosen to start against the Bairns but picked up an early yellow after flattening home keeper Michael McGovern before giving away a string of fouls.
Fearing referee Steven McLean might hand him a second booking, McInnes decided to take no chances as he threw on Vernon in Zola's place after just half an hour.
But the Englishman - who netted the winner in Saturday's Scottish Premiership win against Inverness after again coming on as a substitute - made the most of his chance as he fired a second-half treble in the Dons' 5-0 win which booked them a quarter-final slot.
McInnes said: "Scott got a bit longer than he was anticipating. We always wanted to get him a good chunk of the game but he got on the pitch a bit quicker thanks to a lot of poor decisions against big Calvin.
"We did not want to run the risk of getting him sent off. But Scott got on and it gave him enough time to get a hat-trick.
"That's him got four goals in two games, but he's probably only had about 80 minutes within that. So he's averaging a goal every 20 minutes right now. You've got to be pleased with that.
"Goals are like a drug to strikers and bring them so much confidence. He has a real spring in his step which is pleasing."
Joe Shaughnessy fired Aberdeen ahead after 22 minutes before Cammy Smith doubled the Dons' lead nine minutes before the break.
Vernon failed to find the net in the 15 minutes he played of the first half but started the second period on fire as he blasted two goals in two minutes before claiming the match ball with a spot-kick after Will Vaulks bundled Peter Pawlett over in the box 17 minutes from time.
Aberdeen were simply fantastic going forward but their Championship hosts were all over the place at the back and Falkirk boss Gary Holt admitted they played a significant role in their own downfall.
"I thought Aberdeen were really good but I thought we stood off them and let them play," he said.
"We looked like we got caught in this mindset that they are the Premier League side and we can't tackle them. Whereas every time we got the ball, there was one or two of their guys ratting about us.
"We try to instill in our players that we have to get after the ball but we didn't and it looked like men against boys."